Die Another Day

Abstract

The hydra was a many-headed monster from Greek mythology that could grow
one or two new heads when one of its heads got cut off.
It was the second task of Hercules to kill this monster.
In an abstract sense a hydra can be modeled by a tree
where the leaves are the heads, and when a
head is cut off some subtrees get duplicated.
Different hydra species differ by the location of subtrees to be duplicated
and by the number of new subtrees grown in each step.
Using some deep mathematics, it had been shown that two
classes of rather restricted hydra species must always die,
independent of the order in which heads are cut off.
In this paper we provide an elementary proof
which actually gives a complete classification
of all hydra species as immortal or doomed.
Now, if Hercules had known this...